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Hedge Fund Risk Profiling:A non-linear approach to assess the risk and optimise

Funds of Hedge Funds allocation.

Université d’Evry, 1-2 Avril 2004

Raphaël DouadyResearch Director, Riskdata®

[email protected] www.riskdata.com +33 1 44 54 35 00

2

Evry, April 1, 2004 Journée Gestion Alternative

Hedge Fund Modelling

The Investor Problem

What is the most likely Hedge Fund behaviour under the various market conditions?

What factor or event can put the Hedge Fund at risk?

Is the risk of a portfolio well diversified across the funds

Goal

Build and Rebalance portfolio of Hedge Funds

Select new Hedge Funds to invest in

3



Hedge Funds form asset class different from others

Apparent Statistical Instability

Structural Non-linearity stemming from Dynamic Trading

Usual market factors inefficient to explain returns

Seldom and imprecise information:

Net Asset Value (weekly or monthly, delayed in all cases)

Exposure and sensitivity report

Position transparency only in some cases

4



Methodology

Determine a set of Factors that define the “Market”

Identify, for each Hedge Fund, the Factors that do impact the returns

Build a Proxy of the fund, as a function of each Selected Factor, or of the subset of them

HF return = Proxy + Prediction error

Proxyt = E(HF returnt | Factort U t-1)

5


What Statistical Model for H.F.

Single factor vs. Multi-factor

Factor choice?

Linear vs. Non-linear

Non-linear modelling?

Instantaneous info vs. Lagged

Number of periods for the Fund? For the Factors?

Return series vs. Integrated series

Extreme moves modelling

6


Evaluation Criteria

Explanatory Power

In-sample modelling error

Fund(t) = f(Factor1(t), …, Factorn(t)) + (t)

calibrated on the whole analysis period

Predictive Power

Out-of-sample modelling error

Fund(t) = f(t-1)(Factor1(t), …, Factorn(t)) + (t)

calibrated on [t0, t - 1]

7


Explanation Power

R-square obtained with a Set of 25 Factors – Linear Reg.

TUNA Hedge Fund Indices

Selection of best combination of 5 factors

Factor set:

S&P500, size/style indicesCorp. Bond and HY indicesUS Libor, bond curve, swap curveMSCI World, Emerging marketsFama-FrenchFX BasketCommodity index, Gold, OilS&P optionsS&P historical and implied VolUS T-bond historical vol

STRATEGY Avg R² 5 fact.#periods

Tuna Long Only Average 96.6% 0.2% 0.1%

Tuna Value Average 91.9% 1.2% 0.5%

Tuna Long/Short Hedged Average 91.2% 13.1% 11.2%

Tuna Equity Hedge Aggregate Average 91.1% 13.1% 11.2%

Tuna Hedge Fund Aggregate Average 90.9% 0.0% 0.0%

Tuna Opportunistic Average 90.8% 1.2% 0.8%

Tuna Aggressive Aggregate Average 90.3% 0.1% 0.0%

Tuna Technology Sector Average 89.2% 0.8% 0.3%

Tuna Short Bias Average 88.2% 0.5% 0.5%

Tuna Event Driven Average 87.7% 2.4% 2.8%

Tuna Aggressive Growth Average 87.5% 0.1% 0.0%

Tuna Fund of Funds Average 86.0% 28.1% 24.4%

Tuna Small/Micro Cap Average 83.5% 0.3% 0.0%

Tuna Healthcare Sector Average 83.2% 0.5% 0.2%

Tuna Other Average 83.2% 1.8% 1.0%

Tuna Emerging Markets Average 82.3% 3.4% 2.4%

Tuna Country Specific Average 81.5% 0.4% 0.7%

Tuna MarketTimer Average 78.9% 1.4% 0.6%

Tuna Fixed Income Average 76.8% 1.7% 2.7%

Tuna Market Neutral Average 74.3% 7.5% 13.0%

Tuna Distressed Average 74.2% 2.2% 3.1%

Tuna Finance Sector Average 73.8% 0.4% 0.1%

Tuna Options Strategies Average 67.4% 0.5% 0.3%

Tuna Short-termTrading Average 66.5% 0.4% 0.2%

Tuna Risk Arbitrage Average 66.1% 1.1% 1.0%

Tuna Regulation D Average 60.9% 0.4% 0.1%

Tuna Relative Value Aggregate Average 60.4% 0.8% 1.6%

Tuna Convertible Arbitrage Average 57.1% 4.3% 6.5%

Tuna Macro Average 54.0% 3.1% 4.3%

Tuna Energy Sector Average 52.1% 0.1% 0.0%

Tuna VC / Private Equity Average 49.8% 0.0% 0.0%

Tuna Fixed Income Arbitrage Average 46.3% 2.4% 4.7%

Tuna Statistical Arbitrage Average 46.0% 0.8% 0.3%

Tuna Other Relative Value Average 44.4% 0.8% 1.6%

Tuna Special Situations Average 43.1% 0.2% 0.0%

Tuna Options Arbitrage Average 38.1% 0.5% 0.3%

Tuna CTA Average 36.2% 4.2% 3.6%

10%

80%

11%

9%

% Funds % AUM

76%

14%

8


Risk Profiling: Pairwise Analysis

Question: Does the Risk Factor significantly impacts the fund returns?

Statistical Inference

Sensitivity (Beta)

Convexity (Gamma)

Directional Sensitivities

Conditional Statistics under Up and Down hypotheses

Long-short Equity Europe

-2%

0%

2%

4%

6%

8%

10%

-25% -20% -15% -10% -5% 0% 5% 10% 15% 20%

STOXX Returns

Fund

Ret

urns

= 0 > 0

Beta = 0 does not imply no exposure to Risk Factor

9


Evaluation Criteria

Prediction Power

Correlation between Predicted Series and Actual Returns

Direction Match Probability

Biased if the the Fund average return is ≠ 0

Unbiased measure: Correlation of Sign Series

Prediction Power P2

P2 = 1 – Var(Error) / Var(Return)

Negatively biased because of Spurious Selections

Var(Error) = Var(Specific) + Var(Spurious)

10


State of the Art

Maximum Correlation

Select, in a set of market factors, the factor that is the most correlated to the fund

Proxy the fund by linear regression with respect to this factor

Factor Model / Style Analysis

Determine a fixed factor set

Size limited to the number of data points

Multi-dimensional regression of the Fund returns on this set

Constrain by positive weights for stability (only with directional funds)

Stepwise Regression

Factor set Not Limited

Exposed to Spurious Selections

Still Linear

11


Testing Procedure

Test Pannel (250 funds)

Directional: 75

Non directional: 64

Arbitrage: 32

Special/Event: 24

Aggregates: 23

Other: 22

Random: 10

Hedge Fund Analysis

3Y slipping window

Monthly returns

[Jan 99 – Dec 01]

to [Jan 01 – Dec 03]

Factor set

~200 factors

Equity, IR, Commodity, FX…

Volatility, Correlation, Trend…

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Max Correlation

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Selection Rate

Prediction Correlation

P2

Threshold

14


Max Correlation: Prediction Correlation1 2 3 4 5 6 7 8 9

Threshold 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Strategy Type Nb Funds Correlation 1 Correlation 2 Correlation 3 Correlation 4 Correlation 5 Correlation 6 Correlation 7 Correlation 8 Correlation 9

Total 240 60% 60% 60% 60% 70% 78% 91% 95% 99%Non directional Non directional 64 53% 53% 53% 53% 60% 67% 60% 89% 0%Long/Short Equity Non directional 18 44% 44% 44% 44% 47% 44% 0% 0% 0%CTA/Managed Futures Non directional 14 0% 0% 0% 0% 0% 0% 0% 0% 0%Market Neutral Non directional 17 57% 57% 57% 57% 57% -100% 0% 0% 0%Technology Sector Non directional 3 56% 56% 56% 56% 56% 66% 32% 89% 0%Healthcare Sector Non directional 3 24% 24% 24% 24% -41% 0% 0% 0% 0%Finance Sector Non directional 3 62% 62% 62% 62% 94% 87% 0% 0% 0%Market Neutral Equity Non directional 5 92% 92% 92% 92% 92% 92% 93% 0% 0%Energy Sector Non directional 1 0% 0% 0% 0% 0% 0% 0% 0% 0%Directional Directional 75 67% 67% 67% 67% 74% 80% 93% 95% 99%Test Directional 14 93% 93% 93% 93% 94% 95% 97% 97% 99%Emerging Markets Directional 9 63% 63% 63% 63% 61% 83% 90% 80% 0%Fixed Income (non-arbitrage) Directional 16 24% 24% 24% 24% 52% 100% 0% 0% 0%Opportunistic Directional 9 47% 47% 47% 47% 55% 59% 0% 0% 0%Long Only Directional 6 87% 87% 87% 87% 85% 85% 91% 95% 99%Country Specific Directional 5 75% 75% 75% 75% 75% 43% 87% 0% 0%Short Bias Directional 4 51% 51% 51% 51% 50% 0% 0% 0% 0%Value Directional 6 65% 65% 65% 65% 69% 84% 78% 0% 0%Small/Micro Cap Directional 4 64% 64% 64% 64% 60% 67% 0% 0% 0%Aggressive Growth Directional 2 43% 43% 43% 43% 44% 33% 0% 0% 0%Aggregate Aggregate 23 23% 23% 23% 23% 45% 62% 0% 0% 0%Fund of Funds Aggregate 17 -13% -13% -13% -13% -77% 0% 0% 0% 0%AGGREGATE Aggregate 3 50% 50% 50% 50% 54% -66% 0% 0% 0%Multi-Strategy Aggregate 2 86% 86% 86% 86% 86% 87% 0% 0% 0%Fund of Funds - Multi-Strategy Aggregate 1 0% 0% 0% 0% 0% 0% 0% 0% 0%Special/Event Special/Event 24 44% 44% 44% 44% 60% 76% 84% 0% 0%Event Driven Special/Event 5 39% 39% 39% 39% 71% 74% 0% 0% 0%Distressed Special/Event 8 65% 65% 65% 65% 87% 79% 84% 0% 0%Merger/Risk Arbitrage Special/Event 6 -3% -3% -3% -3% 47% 0% 0% 0% 0%Regulation D Special/Event 2 0% 0% 0% 0% 0% 0% 0% 0% 0%Special Situations Special/Event 3 61% 61% 61% 61% 3% 0% 0% 0% 0%Arbitrage Arbitrage 32 82% 82% 82% 82% 82% 82% 43% 0% 0%Convertible Arbitrage Arbitrage 11 0% 0% 0% 0% 0% 0% 0% 0% 0%Fixed Income Arbitrage Arbitrage 7 0% 0% 0% 0% 0% 0% 0% 0% 0%Other Arbitrage Arbitrage 5 0% 0% 0% 0% 0% 0% 0% 0% 0%Statistical Arbitrage Arbitrage 8 82% 82% 82% 82% 82% 82% 43% 0% 0%Options Strategies Arbitrage 1 0% 0% 0% 0% 0% 0% 0% 0% 0%Options Arbitrage Arbitrage 0 0% 0% 0% 0% 0% 0% 0% 0% 0%Other Other 22 66% 66% 66% 66% 64% 61% 0% 0% 0%Macro Other 9 74% 74% 74% 74% 74% 72% 0% 0% 0%Other Other 7 67% 67% 67% 67% 57% 51% 0% 0% 0%Short-term Trading Other 3 0% 0% 0% 0% 0% 0% 0% 0% 0%Market Timer Other 2 48% 48% 48% 48% 0% 0% 0% 0% 0%VC Private Equity Other 1 100% 100% 100% 100% 0% 0% 0% 0% 0%Random Random 10 0% 0% 0% 0% 0% 0% 0% 0% 0%

15


Max Correlation: Selection RateThreshold 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Strategy Type Nb Funds Correlation 1 Correlation 2 Correlation 3 Correlation 4 Correlation 5 Correlation 6 Correlation 7 Correlation 8

Total 240 27% 27% 27% 27% 18% 11% 6% 4%Non directional Non directional 64 18% 18% 18% 18% 10% 5% 1% 0%Long/Short Equity Non directional 18 28% 28% 28% 28% 11% 4% 0% 0%CTA/Managed Futures Non directional 14 0% 0% 0% 0% 0% 0% 0% 0%Market Neutral Non directional 17 12% 12% 12% 12% 5% 0% 0% 0%Technology Sector Non directional 3 52% 52% 52% 52% 52% 38% 17% 8%Healthcare Sector Non directional 3 15% 15% 15% 15% 7% 0% 0% 0%Finance Sector Non directional 3 42% 42% 42% 42% 29% 18% 0% 0%Market Neutral Equity Non directional 5 16% 16% 16% 16% 16% 16% 8% 0%Energy Sector Non directional 1 0% 0% 0% 0% 0% 0% 0% 0%Directional Directional 75 49% 49% 49% 49% 37% 25% 15% 10%Test Directional 14 56% 56% 56% 56% 53% 50% 45% 43%Emerging Markets Directional 9 58% 58% 58% 58% 31% 19% 13% 6%Fixed Income (non-arbitrage) Directional 16 18% 18% 18% 18% 12% 1% 0% 0%Opportunistic Directional 9 41% 41% 41% 41% 23% 5% 0% 0%Long Only Directional 6 77% 77% 77% 77% 74% 68% 35% 16%Country Specific Directional 5 62% 62% 62% 62% 62% 48% 33% 0%Short Bias Directional 4 41% 41% 41% 41% 10% 0% 0% 0%Value Directional 6 67% 67% 67% 67% 43% 22% 6% 0%Small/Micro Cap Directional 4 59% 59% 59% 59% 47% 25% 0% 0%Aggressive Growth Directional 2 79% 79% 79% 79% 52% 29% 2% 0%Aggregate Aggregate 23 21% 21% 21% 21% 9% 3% 0% 0%Fund of Funds Aggregate 17 15% 15% 15% 15% 2% 0% 0% 0%AGGREGATE Aggregate 3 43% 43% 43% 43% 29% 4% 0% 0%Multi-Strategy Aggregate 2 46% 46% 46% 46% 46% 31% 2% 0%Fund of Funds - Multi-Strategy Aggregate 1 0% 0% 0% 0% 0% 0% 0% 0%Special/Event Special/Event 24 21% 21% 21% 21% 10% 4% 1% 0%Event Driven Special/Event 5 32% 32% 32% 32% 16% 11% 0% 0%Distressed Special/Event 8 21% 21% 21% 21% 9% 6% 4% 0%Merger/Risk Arbitrage Special/Event 6 16% 16% 16% 16% 8% 0% 0% 0%Regulation D Special/Event 2 0% 0% 0% 0% 0% 0% 0% 0%Special Situations Special/Event 3 28% 28% 28% 28% 14% 0% 0% 0%Arbitrage Arbitrage 32 3% 3% 3% 3% 2% 2% 1% 0%Convertible Arbitrage Arbitrage 11 0% 0% 0% 0% 0% 0% 0% 0%Fixed Income Arbitrage Arbitrage 7 0% 0% 0% 0% 0% 0% 0% 0%Other Arbitrage Arbitrage 5 0% 0% 0% 0% 0% 0% 0% 0%Statistical Arbitrage Arbitrage 8 10% 10% 10% 10% 10% 10% 3% 0%Options Strategies Arbitrage 1 4% 4% 4% 4% 0% 0% 0% 0%Options Arbitrage Arbitrage 0 0% 0% 0% 0% 0% 0% 0% 0%Other Other 22 13% 13% 13% 13% 9% 2% 0% 0%Macro Other 9 8% 8% 8% 8% 8% 3% 0% 0%Other Other 7 23% 23% 23% 23% 18% 4% 0% 0%Short-term Trading Other 3 0% 0% 0% 0% 0% 0% 0% 0%Market Timer Other 2 27% 27% 27% 27% 2% 0% 0% 0%VC Private Equity Other 1 8% 8% 8% 8% 0% 0% 0% 0%Random Random 10 0% 0% 0% 0% 0% 0% 0% 0%

16


Stepwise Regression: Prediction CorrelationThreshold 1.5 2.7 5 10 25 50

Strategy Type Nb Funds Stepwise L 1 Stepwise L 2 Stepwise L 3 Stepwise L 4 Stepwise L 5 Stepwise L 6

Total 240 36% 36% 39% 40% 39% 38%Non directional Non directional 64 33% 33% 33% 33% 31% 30%Long/Short Equity Non directional 18 31% 31% 29% 26% 28% 28%CTA/Managed Futures Non directional 14 29% 29% 30% 36% 31% 31%Market Neutral Non directional 17 30% 30% 28% 24% 25% 24%Technology Sector Non directional 3 43% 41% 35% 36% 20% 20%Healthcare Sector Non directional 3 7% 6% 22% 33% 41% 41%Finance Sector Non directional 3 60% 60% 57% 62% 44% 40%Market Neutral Equity Non directional 5 49% 51% 65% 61% 55% 56%Energy Sector Non directional 1 48% 47% 47% 44% 44% 44%Directional Directional 75 54% 54% 58% 64% 62% 62%Test Directional 14 91% 92% 93% 94% 94% 94%Emerging Markets Directional 9 43% 43% 46% 60% 58% 58%Fixed Income (non-arbitrage) Directional 16 29% 29% 35% 46% 44% 44%Opportunistic Directional 9 40% 39% 42% 42% 31% 31%Long Only Directional 6 78% 78% 80% 86% 89% 88%Country Specific Directional 5 41% 42% 47% 54% 56% 56%Short Bias Directional 4 70% 70% 71% 71% 76% 76%Value Directional 6 59% 60% 60% 66% 68% 67%Small/Micro Cap Directional 4 45% 46% 55% 59% 54% 52%Aggressive Growth Directional 2 42% 42% 46% 49% 31% 31%Aggregate Aggregate 23 49% 50% 48% 46% 40% 39%Fund of Funds Aggregate 17 44% 45% 44% 45% 39% 39%AGGREGATE Aggregate 3 74% 74% 68% 66% 55% 54%Multi-Strategy Aggregate 2 81% 83% 82% 87% 85% 85%Fund of Funds - Multi-Strategy Aggregate 1 32% 32% 27% -21% -33% -33%Special/Event Special/Event 24 33% 33% 41% 42% 39% 39%Event Driven Special/Event 5 53% 54% 59% 60% 55% 55%Distressed Special/Event 8 26% 26% 35% 43% 45% 45%Merger/Risk Arbitrage Special/Event 6 41% 42% 37% 19% 11% 11%Regulation D Special/Event 2 -26% -33% 19% 34% 37% 37%Special Situations Special/Event 3 28% 28% 45% 63% 60% 60%Arbitrage Arbitrage 32 13% 12% 12% 7% 7% 7%Convertible Arbitrage Arbitrage 11 16% 16% 15% 3% 5% 5%Fixed Income Arbitrage Arbitrage 7 6% 8% 6% 2% 3% 3%Other Arbitrage Arbitrage 5 0% 0% 0% 1% 11% 11%Statistical Arbitrage Arbitrage 8 17% 16% 15% 14% 12% 12%Options Strategies Arbitrage 1 45% 42% 63% 39% 14% 15%Options Arbitrage Arbitrage 0 0% 0% 0% 0% 0% 0%Other Other 22 3% 4% 10% 13% 12% 12%Macro Other 9 1% 2% 3% 5% 3% 4%Other Other 7 28% 28% 33% 30% 30% 30%Short-term Trading Other 3 -30% -23% -26% -17% -19% -19%Market Timer Other 2 -42% -43% 7% 45% 47% 47%VC Private Equity Other 1 32% 33% 11% -23% -36% -36%Random Random 10 10% 12% 9% 0% 0% 1%

17


Stepwise Regression: P2Threshold 1.5 2.7 5 10 25 50

Strategy Type Nb Funds Stepwise L 1 Stepwise L 2 Stepwise L 3 Stepwise L 4 Stepwise L 5 Stepwise L 6

Total 240 -50% -49% -34% -11% -8% -8%Non directional Non directional 64 -65% -65% -52% -24% -21% -22%Long/Short Equity Non directional 18 -67% -67% -56% -39% -31% -31%CTA/Managed Futures Non directional 14 -73% -73% -53% -7% -5% -5%Market Neutral Non directional 17 -65% -65% -57% -34% -24% -25%Technology Sector Non directional 3 -32% -31% -9% 7% -23% -23%Healthcare Sector Non directional 3 -100% -100% -62% -40% -46% -46%Finance Sector Non directional 3 -58% -57% -19% -1% -10% -17%Market Neutral Equity Non directional 5 -24% -26% -44% -13% -20% -20%Energy Sector Non directional 1 -100% -100% -100% -1% -1% -1%Directional Directional 75 -19% -17% -3% 21% 23% 23%Test Directional 14 76% 77% 80% 83% 83% 81%Emerging Markets Directional 9 -54% -55% -44% 1% 9% 9%Fixed Income (non-arbitrage) Directional 16 -69% -69% -44% -8% -7% -6%Opportunistic Directional 9 -59% -61% -43% -22% -33% -30%Long Only Directional 6 56% 54% 60% 73% 79% 78%Country Specific Directional 5 -64% -63% -29% -3% 17% 18%Short Bias Directional 4 -20% -19% 8% 23% 50% 50%Value Directional 6 -8% -5% 11% 26% 35% 35%Small/Micro Cap Directional 4 -14% -13% -6% 11% 4% 4%Aggressive Growth Directional 2 -57% -59% -67% -17% -51% -51%Aggregate Aggregate 23 -54% -53% -45% -22% -21% -22%Fund of Funds Aggregate 17 -65% -64% -53% -29% -23% -24%AGGREGATE Aggregate 3 -13% -7% -20% 21% -14% -15%Multi-Strategy Aggregate 2 65% 69% 68% 67% 63% 63%Fund of Funds - Multi-Strategy Aggregate 1 -100% -100% -100% -100% -100% -100%Special/Event Special/Event 24 -53% -54% -29% -9% -9% -9%Event Driven Special/Event 5 -38% -35% -3% 9% -1% -1%Distressed Special/Event 8 -34% -35% -10% 16% 18% 19%Merger/Risk Arbitrage Special/Event 6 -82% -82% -76% -71% -65% -65%Regulation D Special/Event 2 -92% -100% -49% -22% -27% -27%Special Situations Special/Event 3 -55% -63% -13% 37% 37% 37%Arbitrage Arbitrage 32 -82% -81% -71% -44% -35% -35%Convertible Arbitrage Arbitrage 11 -71% -71% -62% -44% -35% -35%Fixed Income Arbitrage Arbitrage 7 -82% -80% -78% -47% -43% -43%Other Arbitrage Arbitrage 5 -94% -90% -93% -49% -28% -28%Statistical Arbitrage Arbitrage 8 -90% -90% -73% -47% -33% -33%Options Strategies Arbitrage 1 -91% -94% 20% 0% -23% -21%Options Arbitrage Arbitrage 0 0% 0% 0% 0% 0% 0%Other Other 22 -80% -79% -63% -43% -41% -40%Macro Other 9 -76% -76% -62% -43% -44% -43%Other Other 7 -71% -71% -48% -27% -28% -28%Short-term Trading Other 3 -100% -100% -100% -80% -80% -80%Market Timer Other 2 -100% -100% -52% -29% 4% 4%VC Private Equity Other 1 -52% -51% -100% -100% -100% -100%Random Random 10 -79% -79% -62% -31% -24% -23%

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Other Selection Methods

Non linear regression: F-test, Log-likelihood

Causality (non linear VARMA): F-test

Cointegration. Non linear factor: ∫ Factt² dt

P2

Direction Match

Joint occurrence of Extreme Moves

19


Selection Method Comparison: Prediction Correlation (1 fact)Threshold 10 0.6 0.6 0.4 0.6 0.5 0.9 0.5 0.7

Strategy Type Nb Funds Stepwise Linear Correlation Regression PLReg PL + Bucket Shape Causality

Causality + Bucket Shape Co-integration Prediction Power

Predicted Direction

Total 240 -11% 59% 4% 26% 46% 48% 82% 34% 7%Non directional Non directional 64 -24% 38% -65% -15% 6% 20% 94% 7% -14%Long/Short Equity Non directional 18 -39% 3% -81% -24% -56% 14% 0% -8% -8%CTA/Managed Futures Non directional 14 -7% 0% -83% -19% 0% -11% 0% 6% -7%Market Neutral Non directional 17 -34% 0% -47% -100% 11% -17% 0% -20% -41%Technology Sector Non directional 3 7% 34% -55% -4% 55% 30% 94% 68% -1%Healthcare Sector Non directional 3 -40% 0% -100% 0% 0% -100% 0% 27% -100%Finance Sector Non directional 3 -1% 22% 0% -4% 40% 34% 0% -37% -71%Market Neutral Equity Non directional 5 -13% 84% -14% 64% 76% 76% 0% 90% 68%Energy Sector Non directional 1 -1% 0% 0% 0% 0% 0% 0% 21% 0%Directional Directional 75 21% 64% 43% 49% 53% 58% 93% 49% 33%Test Directional 14 83% 91% 62% 77% 79% 93% 97% 83% 85%Emerging Markets Directional 9 1% 66% 68% 39% 60% 38% 0% 11% -20%Fixed Income (non-arbitrage) Directional 16 -8% 0% -87% -15% -13% -44% 0% 15% 2%Opportunistic Directional 9 -22% -9% -44% 3% -1% 39% 0% 0% -11%Long Only Directional 6 73% 66% 88% 69% 70% 72% 98% 73% 60%Country Specific Directional 5 -3% 20% 65% 66% 59% 54% -45% 36% -28%Short Bias Directional 4 23% 0% 58% 32% 30% 52% 0% 69% 46%Value Directional 6 26% 69% -55% 18% 6% 14% 0% 24% 32%Small/Micro Cap Directional 4 11% 42% -100% -20% 37% 61% 0% 30% 17%Aggressive Growth Directional 2 -17% -13% -100% -31% -10% -29% 0% 35% 13%Aggregate Aggregate 23 -22% 49% -84% -24% 37% 23% -100% 16% -32%Fund of Funds Aggregate 17 -29% 0% -100% -48% 17% -30% -100% -4% -42%AGGREGATE Aggregate 3 21% -36% -7% -96% 60% 55% 0% 42% -63%Multi-Strategy Aggregate 2 67% 66% 0% 70% 52% 51% 0% 69% 59%Fund of Funds - Multi-Strategy Aggregate 1 -100% 0% 0% 0% 0% 0% 0% 0% 0%Special/Event Special/Event 24 -9% 45% -71% -18% 26% -29% -100% 17% -8%Event Driven Special/Event 5 9% 33% -100% -34% 16% -37% 0% 25% -10%Distressed Special/Event 8 16% 60% -24% 24% 69% 5% 0% 42% 2%Merger/Risk Arbitrage Special/Event 6 -71% 0% 0% -5% -100% -100% -100% -7% 30%Regulation D Special/Event 2 -22% 0% 0% 0% 0% 0% 0% 0% -100%Special Situations Special/Event 3 37% 0% -100% 0% 0% 0% 0% -5% -28%Arbitrage Arbitrage 32 -44% 51% -54% -80% 49% 47% 0% -17% -43%Convertible Arbitrage Arbitrage 11 -44% 0% -41% -100% 0% 0% 0% -100% -51%Fixed Income Arbitrage Arbitrage 7 -47% 0% -65% -100% 0% 0% 0% -54% -25%Other Arbitrage Arbitrage 5 -49% 0% -52% -93% 0% 0% 0% 0% -100%Statistical Arbitrage Arbitrage 8 -47% 51% -48% -26% 49% 47% 0% 57% -11%Options Strategies Arbitrage 1 0% 0% 0% 0% 0% 0% 0% 0% 0%Options Arbitrage Arbitrage 0 0% 0% 0% 0% 0% 0% 0% 0% 0%Other Other 22 -43% -5% -66% -26% -4% 11% 65% 9% -32%Macro Other 9 -43% 48% -100% 20% 62% 54% 0% 13% 14%Other Other 7 -27% -57% -32% -82% -68% -14% 0% 21% -53%Short-term Trading Other 3 -80% 0% -100% 0% -100% 0% 65% -46% -100%Market Timer Other 2 -29% 0% 0% 23% 0% 0% 0% 47% -40%VC Private Equity Other 1 -100% 0% 0% 0% 0% 0% 0% 0% -100%Random Random 10 -31% 0% -100% 0% 0% 0% 0% 0% -30%

20


Selection Method Comparison: Prediction CorrelationThreshold 10 0.6 0.6 0.4 0.6 0.5 0.9 0.5 0.7

Strategy Type Nb Funds Stepwise PLCorrelation Multi

Regression PL Multi

Reg PL + Bucket Shape Multi Causality Multi

Causality + Bucket Shape Multi

Co-integration Multi

Prediction Power Multi

Predicted Direction Multi

Total 240 -12% 60% 2% 29% 48% 48% 80% 32% 3%Non directional Non directional 64 -30% 43% -54% -2% 14% 36% 94% -5% -19%Long/Short Equity Non directional 18 -38% 0% -67% -22% -47% 33% 0% -14% -16%CTA/Managed Futures Non directional 14 -19% 0% -83% -19% 0% -19% 0% -49% -25%Market Neutral Non directional 17 -39% 0% -47% -100% 15% -7% 0% -23% -49%Technology Sector Non directional 3 -6% 46% -48% 44% 71% 63% 94% 66% 37%Healthcare Sector Non directional 3 -42% 0% -45% -18% 0% -100% 0% 55% -86%Finance Sector Non directional 3 -15% 22% 0% 34% 30% 31% 0% -37% -42%Market Neutral Equity Non directional 5 -21% 92% 1% 90% 92% 91% 0% 81% 43%Energy Sector Non directional 1 -34% 0% 0% 0% 0% 0% 0% 21% -100%Directional Directional 75 22% 65% 41% 50% 55% 60% 94% 48% 32%Test Directional 14 83% 92% 63% 79% 81% 93% 98% 81% 76%Emerging Markets Directional 9 8% 62% 66% 39% 63% 37% 0% 20% -20%Fixed Income (non-arbitrage) Directional 16 -6% -100% -87% -24% -12% -33% 0% 15% -6%Opportunistic Directional 9 -17% 0% -44% -7% 20% 36% 0% -10% -12%Long Only Directional 6 71% 74% 84% 74% 79% 81% 98% 83% 72%Country Specific Directional 5 -1% 20% 65% 66% 46% 42% -45% 17% -20%Short Bias Directional 4 17% 0% 58% 21% 39% 68% 0% 69% 65%Value Directional 6 32% 70% -55% 18% 11% 15% 0% 29% 31%Small/Micro Cap Directional 4 11% 45% -100% 12% 18% 51% 0% 32% 35%Aggressive Growth Directional 2 -12% -15% -100% -27% -43% -24% 0% 16% -25%Aggregate Aggregate 23 -23% 48% -60% -23% 27% 1% 15% 21% -32%Fund of Funds Aggregate 17 -28% 0% -60% -37% -7% -28% 15% 7% -43%AGGREGATE Aggregate 3 13% -76% -7% -95% 37% -23% 0% 30% -43%Multi-Strategy Aggregate 2 64% 72% 0% 70% 68% 71% 0% 70% 66%Fund of Funds - Multi-Strategy Aggregate 1 -100% 0% -100% 0% 0% 0% 0% 0% -44%Special/Event Special/Event 24 -13% 37% -31% 12% 46% -14% -100% 26% -8%Event Driven Special/Event 5 0% 17% -30% -6% 33% 3% 0% 46% -5%Distressed Special/Event 8 16% 60% -24% 24% 66% -7% 0% -3% 16%Merger/Risk Arbitrage Special/Event 6 -79% 0% 30% 33% 59% -100% -100% 31% -19%Regulation D Special/Event 2 -29% 0% 0% 0% 0% 0% 0% 0% -44%Special Situations Special/Event 3 39% 0% -100% 0% 14% 0% 0% 32% -18%Arbitrage Arbitrage 32 -49% 47% -54% -63% 57% 51% 0% -21% -45%Convertible Arbitrage Arbitrage 11 -48% 0% -41% -100% 0% 0% 0% -100% -53%Fixed Income Arbitrage Arbitrage 7 -50% 0% -68% -100% 0% 0% 0% -62% -37%Other Arbitrage Arbitrage 5 -64% 0% -49% -93% 0% 0% 0% 0% -100%Statistical Arbitrage Arbitrage 8 -46% 47% -40% 25% 57% 51% 0% 64% -11%Options Strategies Arbitrage 1 -12% 0% 0% 0% 0% 0% 0% 0% 0%Options Arbitrage Arbitrage 0 0% 0% 0% 0% 0% 0% 0% 0% 0%Other Other 22 -43% -5% -81% -15% 13% -7% 46% -8% -40%Macro Other 9 -39% 48% -100% 47% 75% -3% 0% -1% 0%Other Other 7 -35% -57% -63% -83% -53% -10% 0% 1% -50%Short-term Trading Other 3 -75% 0% -100% 0% -100% 0% 65% -66% -100%Market Timer Other 2 -26% 0% 0% 23% 0% 0% 23% 47% -46%VC Private Equity Other 1 -79% 0% 0% 0% 0% 0% 0% 0% -100%Random Random 10 -27% 0% -100% 0% 0% 0% 0% 0% -26%

21


Selection Method Comparison: Selection RateThreshold 10 0.6 0.6 0.4 0.6 0.5 0.9 0.5

Strategy Type Nb Funds Stepwise Linear Correlation Regression PLReg PL + Bucket Shape Causality

Causality + Bucket Shape Co-integration Prediction Power

Total 240 76% 11% 12% 18% 18% 19% 5% 27%Non directional Non directional 64 75% 5% 9% 11% 9% 10% 0% 19%Long/Short Equity Non directional 18 78% 4% 11% 14% 13% 13% 0% 22%CTA/Managed Futures Non directional 14 79% 0% 3% 6% 0% 2% 0% 13%Market Neutral Non directional 17 76% 0% 8% 4% 3% 5% 0% 13%Technology Sector Non directional 3 79% 38% 35% 47% 40% 51% 7% 51%Healthcare Sector Non directional 3 54% 0% 15% 1% 1% 4% 0% 11%Finance Sector Non directional 3 79% 18% 0% 19% 26% 21% 0% 36%Market Neutral Equity Non directional 5 59% 16% 9% 16% 16% 16% 0% 17%Energy Sector Non directional 1 79% 0% 0% 4% 0% 0% 0% 13%Directional Directional 75 78% 25% 21% 37% 37% 39% 11% 46%Test Directional 14 79% 50% 63% 75% 73% 71% 54% 75%Emerging Markets Directional 9 77% 19% 18% 25% 25% 29% 0% 44%Fixed Income (non-arbitrage) Directional 16 78% 1% 9% 14% 9% 7% 0% 21%Opportunistic Directional 9 77% 5% 3% 13% 15% 22% 0% 24%Long Only Directional 6 77% 68% 29% 67% 72% 72% 11% 74%Country Specific Directional 5 78% 48% 18% 45% 52% 48% 4% 51%Short Bias Directional 4 78% 0% 9% 45% 43% 42% 0% 53%Value Directional 6 78% 22% 6% 25% 28% 38% 0% 53%Small/Micro Cap Directional 4 77% 25% 4% 31% 47% 59% 0% 46%Aggressive Growth Directional 2 79% 29% 21% 29% 33% 42% 0% 42%Aggregate Aggregate 23 73% 3% 3% 9% 9% 13% 1% 24%Fund of Funds Aggregate 17 78% 0% 3% 6% 6% 6% 1% 21%AGGREGATE Aggregate 3 57% 4% 4% 17% 17% 33% 0% 32%Multi-Strategy Aggregate 2 46% 31% 4% 31% 33% 42% 0% 44%Fund of Funds - Multi-Strategy Aggregate 1 79% 0% 0% 0% 0% 0% 0% 4%Special/Event Special/Event 24 74% 4% 6% 4% 7% 5% 1% 17%Event Driven Special/Event 5 79% 11% 9% 12% 14% 13% 0% 27%Distressed Special/Event 8 79% 6% 6% 2% 8% 5% 0% 13%Merger/Risk Arbitrage Special/Event 6 79% 0% 1% 3% 3% 2% 4% 9%Regulation D Special/Event 2 50% 0% 4% 4% 0% 2% 0% 0%Special Situations Special/Event 3 57% 0% 10% 0% 3% 1% 0% 39%Arbitrage Arbitrage 32 77% 2% 10% 8% 2% 2% 0% 7%Convertible Arbitrage Arbitrage 11 79% 0% 9% 8% 0% 0% 0% 3%Fixed Income Arbitrage Arbitrage 7 77% 0% 22% 12% 0% 0% 0% 13%Other Arbitrage Arbitrage 5 79% 0% 3% 5% 0% 0% 0% 2%Statistical Arbitrage Arbitrage 8 74% 10% 7% 9% 9% 9% 1% 10%Options Strategies Arbitrage 1 79% 0% 8% 0% 0% 0% 0% 0%Options Arbitrage Arbitrage 0 0% 0% 0% 0% 0% 0% 0% 0%Other Other 22 74% 2% 5% 6% 4% 8% 1% 14%Macro Other 9 75% 3% 2% 6% 6% 7% 0% 17%Other Other 7 79% 4% 8% 8% 5% 15% 0% 15%Short-term Trading Other 3 78% 0% 14% 0% 4% 0% 7% 14%Market Timer Other 2 73% 0% 0% 8% 0% 0% 0% 6%VC Private Equity Other 1 38% 0% 0% 0% 0% 0% 4% 0%Random Random 10 79% 0% 4% 1% 0% 0% 0% 0%

22


Selection Method Comparison: Direction MatchThreshold 0.5 0.7 0.5 0

Strategy Type Nb FundsPrediction Power Multi

Predicted Direction Multi

Causality Multi 5

RegPL AND Caus. AND BS Multi

Total 240 57% 49% 57% 68%Non directional Non directional 64 41% 37% 38% 64%Long/Short Equity Non directional 18 44% 32% 29% 58%CTA/Managed Futures Non directional 14 24% 46% 21% 62%Market Neutral Non directional 17 46% 24% 37% 0%Technology Sector Non directional 3 62% 67% 70% 67%Healthcare Sector Non directional 3 100% 50% 3% 87%Finance Sector Non directional 3 -27% -56% 60% 74%Market Neutral Equity Non directional 5 76% 52% 59% 59%Energy Sector Non directional 1 0% 0% 0% 0%Directional Directional 75 65% 60% 66% 76%Test Directional 14 94% 90% 93% 95%Emerging Markets Directional 9 43% 28% 54% 52%Fixed Income (non-arbitrage) Directional 16 34% 27% 39% -11%Opportunistic Directional 9 18% 39% 36% 72%Long Only Directional 6 86% 81% 83% 83%Country Specific Directional 5 54% 54% 72% 75%Short Bias Directional 4 68% 57% 72% 84%Value Directional 6 61% 42% 54% 86%Small/Micro Cap Directional 4 30% 67% 57% 51%Aggressive Growth Directional 2 55% 57% -7% 33%Aggregate Aggregate 23 44% 28% 44% 4%Fund of Funds Aggregate 17 42% 22% 40% -36%AGGREGATE Aggregate 3 46% 35% 51% 42%Multi-Strategy Aggregate 2 50% 54% 55% 64%Fund of Funds - Multi-Strategy Aggregate 1 0% 0% 0% 0%Special/Event Special/Event 24 38% 37% 45% -15%Event Driven Special/Event 5 12% 32% 58% 3%Distressed Special/Event 8 52% 21% 38% 0%Merger/Risk Arbitrage Special/Event 6 73% 65% 73% -100%Regulation D Special/Event 2 0% 0% 0% 0%Special Situations Special/Event 3 38% 30% 10% 0%Arbitrage Arbitrage 32 69% 76% 68% 93%Convertible Arbitrage Arbitrage 11 0% 0% -52% 0%Fixed Income Arbitrage Arbitrage 7 50% 0% 0% 0%Other Arbitrage Arbitrage 5 0% 0% 0% 0%Statistical Arbitrage Arbitrage 8 97% 76% 93% 93%Options Strategies Arbitrage 1 0% 0% 0% 0%Options Arbitrage Arbitrage 0 0% 0% 0% 0%Other Other 22 38% 34% 34% 79%Macro Other 9 17% 44% 26% 65%Other Other 7 66% 46% 43% 100%Short-term Trading Other 3 0% 9% 27% 0%Market Timer Other 2 0% 38% 0% 0%VC Private Equity Other 1 0% -100% 0% 0%Random Random 10 0% -25% 58% 0%

23


Missed Selections

P2 Threshold 40%Tol 10%

Thresholds 1 0.95 0.5 0.6 0.4 3 0.5 0.8 0.8 0.8

Strategy Type Nb FundsBucket Average

Bucket Shape

Correlation R2

Regression PL

Quadratic Regression Causality

Cointegration Lin Rev

Cointegration Quad Rev

Cointegration Quadratic

Total 1178 0.95 0.52 0.36 0.37 0.25 0.34 0.94 0.93 0.51Long/Short Equity Non directional 156 0.72 0.44 0.36 0.26 0.23 0.40 1.26 0.72 0.43Market Neutral Non directional 85 0.89 0.58 0.24 0.52 0.13 0.25 0.46 0.93 0.58CTA/Managed Futures Non directional 73 0.64 0.55 0.32 0.33 0.21 0.23 0.45 0.68 0.45Market Neutral Equity Non directional 18 0.39 0.28 0.30 0.06 0.17 0.17 0.67 0.28 0.28Healthcare Sector Non directional 9 1.56 1.33 0.44 0.56 0.33 0.67 1.22 1.22 1.11Technology Sector Non directional 8 0.13 0.13 1.63 0.00 1.25 1.38 3.50 0.13 0.13Finance Sector Non directional 6 1.50 0.67 1.33 0.50 0.83 0.83 2.17 1.67 0.83Energy Sector Non directional 1 5.00 4.00 0.00 1.00 0.00 0.00 0.00 5.00 4.00Fund of Funds Aggregate 329 0.93 0.52 0.35 0.37 0.27 0.40 0.82 0.91 0.52AGGREGATE Aggregate 4 4.50 2.75 1.25 1.75 1.00 1.00 3.00 4.00 2.50Fund of Funds - Multi-Strategy Aggregate 4 1.50 0.75 0.50 0.25 0.00 0.75 1.25 1.75 0.75Multi-Strategy Aggregate 2 0.00 0.00 0.00 0.00 0.00 1.00 3.00 0.00 0.00Test Directional 93 2.14 0.73 0.64 0.44 0.42 0.47 2.62 2.06 0.72Emerging Markets Directional 40 0.78 0.60 0.45 0.48 0.40 0.43 1.30 0.78 0.58Fixed Income (non-arbitrage) Directional 19 0.47 0.26 0.20 0.32 0.05 0.11 0.37 0.53 0.26Opportunistic Directional 16 0.56 0.38 0.59 0.38 0.56 0.63 1.44 0.63 0.38Long Only Directional 10 1.10 0.50 1.67 0.30 0.30 0.40 4.10 1.30 0.40Value Directional 9 1.22 0.89 0.78 0.67 1.11 1.11 2.33 1.00 0.78Country Specific Directional 7 1.00 0.43 0.40 0.43 0.29 0.43 0.86 1.29 0.57Short Bias Directional 7 1.43 0.86 3.40 0.86 2.57 1.71 5.86 1.43 0.57Small/Micro Cap Directional 7 2.14 1.29 0.29 0.43 0.29 0.71 1.43 2.00 0.86Aggressive Growth Directional 4 1.50 1.25 0.25 0.75 0.25 1.00 1.00 1.50 1.50Event Driven Special/Event 42 0.93 0.50 0.32 0.50 0.29 0.31 0.74 0.88 0.48Distressed Special/Event 30 0.70 0.37 0.33 0.27 0.20 0.33 0.47 0.57 0.43Merger/Risk Arbitrage Special/Event 18 0.67 0.39 0.47 0.28 0.17 0.22 0.50 0.61 0.28Regulation D Special/Event 5 0.20 0.40 0.00 0.00 0.00 0.00 0.00 0.40 0.20Special Situations Special/Event 2 0.50 0.50 1.50 0.50 1.50 1.00 1.00 0.50 0.50Convertible Arbitrage Arbitrage 54 1.11 0.57 0.15 0.46 0.00 0.06 0.09 1.02 0.52Fixed Income Arbitrage Arbitrage 22 1.27 0.64 0.31 0.55 0.09 0.09 0.23 1.05 0.64Other Arbitrage Arbitrage 13 1.46 0.85 0.00 0.69 0.00 0.00 0.08 1.46 0.92Short-term Trading Arbitrage 7 1.43 0.71 0.14 0.43 0.14 0.29 0.57 1.14 0.14Options Arbitrage Arbitrage 6 2.00 1.00 0.86 1.33 1.00 1.17 1.83 1.67 1.33Statistical Arbitrage Arbitrage 6 3.00 1.00 0.00 1.50 0.17 0.17 0.50 2.83 2.00Options Strategies Arbitrage 2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00Macro Other 39 1.49 0.90 0.10 0.56 0.03 0.13 0.44 1.54 0.87Other Other 22 0.64 0.32 0.45 0.09 0.36 0.50 0.95 0.73 0.41Market Timer Other 3 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00Random Random 100 0.08 0.03 0.02 0.04 0.00 0.02 0.05 0.08 0.05

A factor is missed, within its class, if 1) Its P2 is maximum in the class and above the threshold 40% and 2) the factor selected by the method in this class has a P2 below this maximum by more than the tolerance 10%.

24


Findings

Classical Linear methods are either often spurious (stepwise regression) or miss essential afctors (correlation)

Non linear modelling is necessary

Statistical factors, such as Hist. Vol., Correl Index, etc. expalin a lot of hedge fund returns

Causality is efficient because of Lagged series

Co-integration is useful to find the “right” factor, but not for prediction capabilities. Dickey-Fuller mean reversion test worsen statistics

Direction match probability test good for “event” type strategies

Large factor shifts should be analysed differently: use the frequency of joint large move occurrence between the fund and the factor.

25


Conclusion

Performance Analysis + Correlations are insufficient for the construction of Portfolios of of Hedge Fund

A Complete Set of Risk Factors contains Factors that replicate Dynamic Strategies

Sensitive to Volatility and Correlation of Assets

Include Non-linear Features

Hedge Funds must be Proxied by Non-linear functions of Factors

Building a Risk Profile is the only way to identify Market Conditions under which Funds over/under-perform

This is also the only way to extract Stable information from Return series

26


Correlation of Long-Short Equity Funds to TUNA LS Index24M slipping period (end indicated)

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

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Glenrock G

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RJL Partne

New Castle

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Seminole C

Crestwood

Standard S

Canterbury

Galleon Om

Knoll Capi

Pangaea Ov

Sandler Co

Gordon Hou

27


Riskdata FoFIX®

journée « gestion alternative et imperfections de marché » hedge fund risk profiling: a...

Documents

risk factor

likely hedge fund behaviour

marchhedge fund risk

fund average return

set of factors

set of market factors

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